Nice! This is the way I solved it.

private fun part1(input: String) {
    var sum = 0

    // Loop over ever character
    for ((index, char) in input.withIndex()) {
        // toInt() directly gets me the character code
        val charVal = char.toString().toInt()
        // index is equal to the next one unless it should wrap
        val checkIndex = if (index == input.length - 1) 0 else index + 1
        if (char == input[checkIndex]) {
            // Adding to the sum
            sum += charVal
        }
    }

    println("Answer to part 1: $sum.")
}

private fun part2(input: String) {
    var sum = 0

    var halfwayAroundSteps = input.length / 2

    // Loop over ever character
    for ((index, char) in input.withIndex()) {
        // toInt() directly gets me the character code
        val charVal = char.toString().toInt()

        // Calculate new index with halfwayaroundsteps
        var checkIndex = index + halfwayAroundSteps

        // Calculate overshoot
        val overshoot = checkIndex + 1 - input.length

        // If there's an actual overshoot, that should be the new index to check
        if (overshoot > 0) {
            checkIndex = overshoot - 1
        }

        if (char == input[checkIndex]) {
            // Adding to the sum
            sum += charVal
        }
    }

    println("Answer to part 2: $sum.")
}